A two-digit number is 7 times the sum of its digits. The number that is formed by reversing its digits is 36 less than original number. What is number?

Question: A two-digit number is 7 times the sum of its digits. The number that is formed by reversing its digits is 36 less than original number. What is number?

Solution:
Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
∴ 10x + y = 7(x + y)
⇔ 3x = 6y
⇔ x = 2y

Number formed by reversing the digits = 10y + x
∴ (10x + y) - (10y + x) = 36
⇒ 9x - 9y = 36
⇒ x - y = 4
⇒ 2y - y = 4
∴ y = 4

So, x = 2y = 2 × 4 = 8
Hence, the number is = 10 × 8 + 4 = 84.